Abstract
SummaryThis paper establishes a novel online fault detection and identification strategy for a class of continuous piecewise affine (PWA) systems, namely, bimodal and trimodal PWA systems. The main contributions with respect to the state‐of‐the‐art are the recursive nature of the proposed scheme and the consideration of parametric uncertainties in both partitions and in subsystems parameters. In order to handle this situation, we recast the continuous PWA into its max‐form representation and we exploit the recursive Newton‐Gauss algorithm on a suitable cost function to derive the adaptive laws to estimate online the unknown subsystem parameters, the partitions, and the loss in control authority for the PWA model. The effectiveness of the proposed methodology is verified via simulations applied to the benchmark example of a wheeled mobile robot.
Highlights
Piecewise affine (PWA) systems constitute a special class of complex systems that has been extensively studied in the literature in many application domains: production control systems,[5] robotics,[6] and flight control systems,[7] among others
In the classical setting, the fault detection and identification (FDI) problem can be reformulated in terms of an estimation problem, ie, it is assumed that faults in the system are reflected in a change of the parameters of the system model.[8]
We evaluate the effectiveness of the online FDI technique on the wheeled mobile robot (WMR) shown in Figure 1 and presented in the work of Nayebpanah et al.[43]
Summary
With the increased demand of reliability for control systems, much attention has been devoted by the control community in fault detection techniques for complex systems.[1,2,3,4] Piecewise affine (PWA) systems constitute a special class of complex (in particular, hybrid) systems that has been extensively studied in the literature in many application domains: production control systems,[5] robotics,[6] and flight control systems,[7] among others. Online FDI algorithms produce unknown system estimates at each time instant, by processing and evaluating the current signals measurements Because of this, they are commonly referred to as recursive FDI algorithms, to be distinguished from the offline or nonrecursive ones. They are commonly referred to as recursive FDI algorithms, to be distinguished from the offline or nonrecursive ones For the latter case, found in the literature as the batch FDI estimation algorithms, all signals' measurements are collected offline over large time interval horizons. Found in the literature as the batch FDI estimation algorithms, all signals' measurements are collected offline over large time interval horizons In both online or offline methods, the unknown parameters are calculated by using optimization techniques on some appropriately chosen cost function.
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